This paper circulates around the core theme of a) Can the denition of f(x) when x 6= 1 be simplied? If yes, what is the simpler expression? together with its essential aspects. It has been reviewed and purchased by the majority of students thus, this paper is rated 4.8 out of 5 points by the students. In addition to this, the price of this paper commences from £ 24. To get this paper written from the scratch, order this assignment now. 100% confidential, 100% plagiarism-free.
Question 1. 3+5=8 marks
b) The equation x2 6x + y2 + 8y = 24 describes a circle.
i `Complete the square` to write the equation in form (x a)2 + (y b)2 = r2
ii Write down the coordinates of the centre of the circle and its radius.
iii What are the coordinates of the uppermost point of the circle?
Question 2. 3+2+4+4=13 marks
Consider the function with piecewise denition
a) Can the denition of f(x) when x 6= 1 be simplied? If yes, what is the simpler expression?
b) Sketch the graph of f(x) carefully for x between -5 and 3.
c) What is the domain of this function? What is its range? Justify your answers.
d) Is f(x) continuous? Assess this property formally.
Question 9. 4+5+2=11 marks
A particle moves along a number line so that its position at time t is given by
s(t) = t3 10t2 + 12t (t 0)
where s is in centimetres and t in seconds.
a) When does the particle change direction ? (i.e. when does its velocity change from nega-
tive to positive or vice versa?)
b) When is the particle moving to the right?
c) What is the furthest left the particle attains?
total 90 marks